Electrochemical Hardness: A Reactivity Descriptor for the Electrocatalytic Activity of mn4 Molecular Catalysts for the Reduction of o2 in Aqueous Media

Molecular catalysts, like metal complexes such as MN<inf>4</inf> or MN<inf>x</inf> molecular catalysts exhibit several reactivity descriptors: (i) the M−O<inf>2</inf> binding energy, (ii) the M(III)OH/(II) formal potential, (iii) the number of d-electrons in the MN4, (iv) the donor (M)-acceptor intermolecular hardness, and (v) π-electron graphene-MN4 delocalization factor. When oxygen reduction reaction (ORR) activity, expressed as (log j)<inf>E</inf> at constant potential, is plotted versus adsorption energy (E<inf>ad</inf>) or versus the formal potential E°’M(III)/(II), the trends exhibit symmetrical volcano correlations. In this work, we consolidate and extend the concept of electrochemical hardness (ΔEh) as a reactivity descriptor for MN<inf>4</inf> molecular catalysts. This descriptor is defined as the potential separation between the two central formal potentials exhibited by surface-anchored MN4 molecular catalysts in the absence of O<inf>2</inf> in aqueous media. The catalytic activity for ORR increases as ΔEh decreases, suggesting that for highly active catalysis, the two redox one-electron reversible processes tend to a minimum or even overlap. All these reactivity descriptors are not independent from each other and are closely related. © 2025